1. Field of the Invention
The present invention relates to the field of alignment methods. In particular, the present invention relates to methods for determining a lateral and angular offset between two rotatable parts.
2. Description of Related Art
The method according to the invention for determining a lateral and angular offset between two tandem-arranged shafts relates to an improvement of the invention described in U.S. Pat. No. 5,026,998 to Hoelzl (based on German patent DE 3911307). An analogously equivalent representation of the invention described in the ""998 patent is to be found in U.S. Pat. No. 5,263,261 to Piety et al. Both publications are hereby incorporated by reference in this application to avoid repetitive disclosure in the present application.
The present invention proceeds from the finding that in the past, a partial problem to be solved consisted in describing two mechanically caused movements or deflections observed, versus an angular measure and possibly subject to some boundary conditions, by means of suitable characteristic parameters. This can be appreciated from the figures of the above named patent specifications. The said movements are regarded as essentially sinusoidal in nature (i.e. varying according to a sine function) and of a predefined periodicity. The problem to be solved resided, inter alia, in determining the said characteristic values of the sinusoidally varying movements (deflections) from a minimum number of measured values that are xe2x80x9cnoisyxe2x80x9d to a certain amount.
The complete solution as taught from the ""998 patent seeks to specify the sinusoidal movements in a single formulation by means of the parameters of a Lissajous ellipse defined by the sinusoidal components of two individual movements. This requires the acquisition of at least five pairs of measured values. At the same time, at least one item of angular information is required to define a spatial reference position for the participating shafts. Moreover, a prescribed direction of rotation of said shafts is to be specified. The associated calculation, according to the ""998 patent, provides a two-dimensional analysis of the Lissajous ellipse, which is to be regarded as a locus.
In contrast, the analysis in accordance with U.S. Pat. No. 5,263,261 to Piety et al. is limited to one-dimensional analysis. That analysis of the participating sinusoidal functions is undertaken twice, and will yield, after combining the results obtained, a result which is the same in principle to the results obtained in the ""998 patent. However, because of the selected mode of procedure, the result obtained using the method of the ""261 patent can be affected by a larger amount of total error, in accordance with a generally known addition theorem for noise factors. It is noted that the following is necessary for carrying out the analysis described in U.S. Pat. No. 5,263,261 (as represented and claimed in ""998 patent as a subset of the method proposed there): simultaneously with the acquisition of the above named movement data, whether by mechanical means or by recording appropriately converted electric signals, at least three angular positions of the participating axles, shafts or the like are to be recorded. Formulated otherwise, this means that in accordance with the ""261 patent, more than only a single angular position serving as an xe2x80x9cinterpolation pointxe2x80x9d is to be acquired and recorded using appropriate measurement technology. As may be gathered from documents published by Pruftechnik AG and CSI, Inc., in order to acquire a plurality of angular positions, electrically or electronically acting inclinometers are employed which have a resolution and reproducibility of approximately one to two angular degrees.
The present invention, now, proceeds from the following consideration: if, as is already known from the two patent specifications cited above, several angular position of the two shafts to be aligned are recorded together with relevant apparent movements or deflections in order to obtain more than only one angular xe2x80x9cinterpolation pointxe2x80x9d, these angular data are already considerably xe2x80x9cnoisyxe2x80x9d. That is to say, the angular data are affected by substantial measurement uncertainties because of the technical properties of the inclinometers used. This poses a problem of its own, and a solution of this problem will yield improved data useful for a subsequent calculation of correction and adjustment values for aligning machines. (Note that this problem does not arise per se in the case of the xe2x80x9cinclinometer-lessxe2x80x9d method known from specification of the ""998 patent, if only one single reference angle is available.) The said problem arises particularly when modem, high resolution CCD or CMOS pixel based sensors are employed for measuring above mentioned movements. Formulated otherwise, the problem and the task at hand can be described as follows: the xe2x80x9cnoisyxe2x80x9d inclinometer data generate a measurement error, whose influence on the desired final result of computation is to be minimized. Therefore, there exists an unfulfilled need for a method for determining a lateral and angular offset between two tandem-arranged shafts which will minimized the measurement and computational error.
The method according to the present invention for determining a lateral and/or angular offset between rotatable parts such as two tandem-arranged shafts, axles, rollers or the like provides, in accordance with the prior art known per se, that at least one measuring pointer rigidly fitted relatively to one of the shafts, axles or rollers, and at least two measuring pick-ups or reference elements assigned to the measuring pointer or pointers and rigidly fitted on a respectively different shaft, axle or roller being used in a plurality of measuring angular positions corresponding to each other in each case from shaft to shaft to generate two mutually independent measuring signals. For this purpose, mechanical, or preferably laser-optical measuring means as measuring pointers, as has already been specified in the cited patent specifications may be used. Although the present invention may be applied to determine a lateral and/or angular offset between rotatable parts such as two tandem-arranged shafts, axles, rollers or the like, a specific embodiment as applied to alignment of tandem-arranged shaft is discussed hereinbelow. However, the present application should not be construed to be limited to such an application but is also applicable to axles, rollers or the like. In the case of the tandem-arranged shafts, the measuring signals relate both to a measuring angular position component, used as a basis, of the (shortest) spacing which the center axes of the shafts possibly have from one another (parallel offset), and of an angular component at which the center axes are offset askew. The measuring signals correspond to said components (that is to say are normally proportional to them), or can be derived from said components. In accordance with the method according to the invention, it is now proposed to obtain improved measuring results in a novel way, specifically by virtue of the fact that
a) the shafts are turned into at least four different, freely selectable measuring angular positions in which measurements are taken,
b) in each angular position, measuring signals affected by measurement uncertainties are picked up and recorded, the measuring signals being provided as measured-value triplets and respectively comprising: the measured angular value of a measuring angular position, a measured value generated by a first measuring device or reference element, and a measured value generated by a second measuring device or reference element,
c) a calculating device, in particular an electronic device (computer) is used to carry out a three-dimensional fitting calculation or adaptation in which the characteristic values are calculated in accordance with a prescribed fitting principle for an elliptical, periodically continued helical curve (elliptical helix), or its approximation by other functions, and
d) the characteristic values of the elliptical helical curve, taking account of at least one of the known angular positions and the direction of rotation of the shafts during rotation into the measuring angular positions, are used by means of the computer to determine the spatial position of the shafts, axles or rollers relative to one another and, if appropriate, correction values for their positional correction for the purpose of eliminating an alignment error which may have been established.
In a preferred embodiment of the method in accordance with the present invention, equipment and/or programs are made available which permit that the xe2x80x9cmethod of least squaresxe2x80x9d is applied as the fitting principle. Instead of the method of least squares (sums of squares), it is also possible to select a mode of procedure in which
a)the measured-value triplets are interpreted as points in a three-dimensional space,
b) the parameters of a helix fitting said points are varied until the sum of all the spacings of said points, or the sum of the squares of all the spacings of said points assumes a minimum value relative to said fitting helix, and
c) the parameters of a fitting helix thus found are used as a basis for a subsequent calculation which will yield values for compensation that may be utilized in a following step to align the two shafts in a more perfect way.
In a further, similar design of the method according to the invention, use being made of a comparable summing rule in which the spacings (which are positive definite, and calculated using normal definitions) of said points from said fitting elliptical helix are raised in each case to a predefined power, the value of which can be selected from approximately 0.5 to 4.5.
The fitting of measured point triplets to a fitting elliptical helix in accordance with the present invention, typically requires a sufficient amount of computer capacity. The basic principles and methods of such fitting calculation are known per se, as shown in the book by R. Ludwig, Methoden der Fehler und Ausgleichsrechnung [Methods For Calculating Errors And Corrections], Library of congress Catalog Card No. 69-17093, published by Vieweg und Sohn, 1969.
Depending on the prescribed computational structure, it can be advantageous for the purpose of making best use of an available computer capacity to carry out the fitting calculation for determining the parameters of an elliptical helix regarded as optimum by using so-called neural networks and/or so-called fuzzy logic, and terminating a current computing run with a sufficiently accurate result when additional iterations of the computing process no longer yield significant changes of the values of the parameters found.
Alternatively, the present problem can also be interpreted in such a way that the parameters xe2x80x9cof two sinusoidal vibrations in spacexe2x80x9d are determined for the purpose of a fitting calculation. If the computer is equipped with an arithmetic unit for calculating integral transformations (Fourier, Hadamard, Haar inter alia), such a device can be used advantageously to solve the problem outlined by means of such integral transformations. In accordance with the present invention, it is advantageous in this case that some of these transformations have the property per se of automatically supplying a best adaptation for the purpose of a fitting calculation. Consequently, the invention also relates to a method in which a fitting calculation is carried out to determine the parameters of an elliptical helix regarded as optimum by using a three-dimensional integral transformation, in particular, a three-dimensional Fourier transformation. Stated in other terms, the invention relates to a method to apply a spatial filtering to an elliptical helix by means of a three dimensional Fourier transform and a corresponding inverse transform, which utilizes only low-numbered terms of the transform to arrive at a spatially filtered elliptical helix, which then, will constitute a basis for further corrective action on machines.
It may be further pointed out that the term xe2x80x9celliptical helixxe2x80x9d employed is also intended to include those special cases in which the general form of an ellipse is no longer recognizable because the geometrical loci of xe2x80x9ccirclexe2x80x9d, xe2x80x9clinexe2x80x9d or xe2x80x9cpointxe2x80x9d are concerned. As is known, these constitute merely special cases of an associated ellipse defined by special parameters, and can therefore be used in general as a basis for a further computing run.
The values calculated using the method according to the invention for adjusting machines or machine characteristics are communicated to an operator either optically or acoustically. In accordance with another aspect of the invention, it is advantageous on the basis of the enhanced accuracy, to have the adjustment carried out by electric tools which are driven by the same computer which has also calculated the relevant correction values. This can be performed by means of open loop control or closed loop control. In the latter case, said electric tool for adjusting machines is actuated until no further improvement is achieved in the adjustment for the machines which are to be aligned with one another. For this purpose, the invention therefore also relates to a method for adjusting machines with laterally or angularly offset axes, which uses correction values found by means of a specific fitting calculation method which is described above for the purpose of specifically varying the position of the machines assigned to the shafts, axles or rollers, or parts thereof, by means of computer connected and electrically driven tools.
These and other objects, features and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments of the invention when viewed in conjunction with the accompanying drawings.